This is a linkpost for http://squirrelinhell.blogspot.com/2016/04/geometric-bayesian-update.html
the stuff on the left whose only job is to put the whole thing into a rectangle.
You are forgetting that it makes it possible to keep the scale of all numerical input/outputs consistent.
Point taken. (I personally prefer odds ratios strongly enough for this kind of thing that keeping the scale consistent doesn't bother me.) You could fix that, kinda, by fixing the side lengths of the "prior" and "posterior" side while allowing the length of the "evidence" side to vary, but that means introducing extra not-so-visible constraints so maybe it's a bit of a cheat.
I have moved this post to my blog: http://squirrelinhell.blogspot.com/2016/04/geometric-bayesian-update.html